Optimal. Leaf size=17 \[ -\frac {(a+b x)^3}{3 a x^3} \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.00, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {37}
\begin {gather*} -\frac {(a+b x)^3}{3 a x^3} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 37
Rubi steps
\begin {align*} \int \frac {(a+b x)^2}{x^4} \, dx &=-\frac {(a+b x)^3}{3 a x^3}\\ \end {align*}
________________________________________________________________________________________
Mathematica [A]
time = 0.00, size = 26, normalized size = 1.53 \begin {gather*} -\frac {a^2}{3 x^3}-\frac {a b}{x^2}-\frac {b^2}{x} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.07, size = 25, normalized size = 1.47
method | result | size |
gosper | \(-\frac {3 x^{2} b^{2}+3 a b x +a^{2}}{3 x^{3}}\) | \(23\) |
norman | \(\frac {-x^{2} b^{2}-a b x -\frac {1}{3} a^{2}}{x^{3}}\) | \(24\) |
risch | \(\frac {-x^{2} b^{2}-a b x -\frac {1}{3} a^{2}}{x^{3}}\) | \(24\) |
default | \(-\frac {b^{2}}{x}-\frac {a^{2}}{3 x^{3}}-\frac {a b}{x^{2}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.27, size = 22, normalized size = 1.29 \begin {gather*} -\frac {3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 1.10, size = 22, normalized size = 1.29 \begin {gather*} -\frac {3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.05, size = 24, normalized size = 1.41 \begin {gather*} \frac {- a^{2} - 3 a b x - 3 b^{2} x^{2}}{3 x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 1.12, size = 22, normalized size = 1.29 \begin {gather*} -\frac {3 \, b^{2} x^{2} + 3 \, a b x + a^{2}}{3 \, x^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 0.04, size = 22, normalized size = 1.29 \begin {gather*} -\frac {\frac {a^2}{3}+a\,b\,x+b^2\,x^2}{x^3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________